Answers
because if you simplify it to write it in the form y=mx +b, you'll get y = x + 6.
So the slope is 1 and y-intercept is 6.
Related Questions
A right rectangular prism has a square base and a height of 9 feet. its volume, v, is 144 cubic feet. what is the length of s, the sides of the base?
Answers
Given that the volume is 144 ft³ and height is 9 ft
volume = base area x height
144 = base area x 9
base area = 144 ÷ 9
base area = 16 ft²
The base is a square which means both sides are of the same length
area = length x length
16 = length²
length = √16
length = 4 ft
s, the side of the base is 4 ft
The length of the sides of the base of a rectangular prism is 4 feet.
Given that, a right rectangular prism has a square base and a height of 9 feet.
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
Volume of a rectangular prism = Area of a base × Height.
Here, the volume of a rectangular prism = 144 cubic feet
Area of base = Area of a square = s²
So, 144 = s² × 9
⇒ s² = 16
⇒ s = 4 feet
Therefore, the length of the sides of the base of a rectangular prism is 4 feet.
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Write the expression as either the sine, cosine, or tangent of a single angle
Answers
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
where in this case,
x = pi/3
y = pi/5
So,
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(pi/3-pi/5) = cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(pi/3-pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(5pi/15-3pi/15)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(2pi/15)
------------------------------------------------------------
The answer is cos(2pi/15) which can be written as [tex]\cos\left(\frac{2\pi}{15}\right)[/tex]
Bob's carpet cleaning company uses the equation y=22x+30 to calculate cost, y, to clean x numbers of rooms. Andy's carpet cleaning company uses the table below to calculate the cost to clean rooms.
Laura needs 5 rooms cleaned. Which company charges less and by how much less?
Answers
Andy charges $135
Andy is cheaper
please help asap! 54 points
Answers
a)
point slope intercept
y + 2 = 4/3(x - 3)
standard form
y + 2 = 4/3(x - 3)
3y + 6 = 4x - 12
- 4x + 3y = -18 ..........this is standard form
Answer is C
y + 2 = 4/3(x - 3); -4x + 3y = -18
point-slope from is
y - (-2) = (4/3)(x - 3)
y + 2 = (4/3) (x - 3) is the equation in point slope form
Standard form is -4x + 3y = -18
The answer is C
A room's length is 3 feet less than twice its width. The area of the room is 135 square feet. What are the room's dimensions?
Answers
Hope this helps:
A= L x W
135 = (2w-3)(W)
135 = (2w squared - 3W)
135 = 2w^2-3w
2w^2-3w-135 = 0
-----
Use the quadratic formula to get:
w = [3 +- sqrt(9 - 4*2*-135)]/4
Positive solution:
w = [3 + sqrt(1089)/4
w = [3 + 33]/4
w = 9 ft
L = 2W-3 = 2*9-3 = 15 ft.
If the width is w, the length is l = 2w-3.
The total area is length x width = w*(2w-3)
Solve
w*(2w-3)=135 to find w.
2w^2-3w-135=0
w = (3 +/- sqrt ( 9 +8*135))/4
The positive solution is
w = ( 3 + 33) /4 = 9 and then l = 15.
The dimensions of room are: Length = 15 feet and Width = 9 feet.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
we have,
A room's length is 3 feet less than twice its width.
The area of the room is 135 square feet.
let the width be x then length = 2x - 3.
So, Area of Room
135 = l w
135 = x (2x- 3)
2x² - 3x - 135= 0
2x² + 15x - 18x - 135 = 0
x (2x+ 15) - 9 (2x- 15)= 0
(2x+ 15)(x- 9)=0
x= -15/2 or x= 9.
Thus, the dimensions of room are:
Length = 2(9)-3 = 15 feet
Width = 9 feet
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A graphic artist earns $22 an hour, and she works 44 hours a week. What is her weekly wage?
A. $154
B. $308
C. $66
D. $968
Answers
Answer:
The answer is option D. The weekly wage is $968.
Step-by-step explanation:
The weekly salary can be found multiplying the earned money per hour and the amount of hours worked in the week:
[tex] Wweek=22\ \$/hr* 44\ hr/week[/tex]
[tex] Wweek=968\ \$/week[/tex]
A sign standing 6 feet tall is situated 18 feet away from a flag pole. at a certain time of day the sign's shadow is 3 feet long and the flagpole's shadow is 24 feet long. how tall is the flagpole?
Answers
On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft
When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.
We can apply trigonometry rules to find height of flagpole.
From small triangle containing sign we can find tangens function:
[tex]tan \alpha = \frac{C}{D} [/tex]
Similarly we can do for large triangle containing flagpole:
[tex]tan \alpha = \frac{A}{B} [/tex]
We see that these two equations have same left sides. This means that their right sides must also be same:
[tex]\frac{C}{D} = \frac{A}{B}[/tex]
We can solve for A:
[tex]CB=AD \\ A= \frac{CB}{D} \\ A= \frac{6*24}{3} \\ A=48 ft[/tex]
Height of flagpole is 48 feet.
Juliana and Maria logged a total of 90 hours working for their dad. Juliana worked 2 hours more than three times as much as Maria. How many hours did Juliana work?
Answers
Juliana worked 68 hours
Explanation:
Assume the hours logged by Juliana is x
Assume the hours logged by Maria is y
We are given that:
1- Total hours logged by both is 90. This means that:
x + y = 90
This equation can be rewritten as:
x = 90 - y ...........> equation I
2- Juliana worked 2 hours more than 3 times as much as Maria. This means that:
x = 3y + 2 ...........> equation II
Substitute with equation I in equation II and solve for y as follows:
x = 3y + 2
90 - y = 3y + 2
88 = 4y
y = 22
Substitute with y in equation I to get x as follows:
x = 90 - y
x = 90 - 22
x = 68
Based on the above:
Hours logged by Juliana = x = 68 hours
Hours logged by Maria = y = 22 hours
Hope this helps :)
Let
x---------> the hours logged by Juliana
y---------> the hours logged by Maria
we know that
[tex]x+y=90[/tex] ---------> equation [tex]1[/tex]
[tex]x=3y+2[/tex] ---------> equation [tex]2[/tex]
Substitute equation [tex]2[/tex] in equation [tex]1[/tex]
[tex](3y+2)+y=90[/tex]
[tex]4y+2=90[/tex]
[tex]4y=90-2[/tex]
[tex]4y=88[/tex]
[tex]y=88/4[/tex]
[tex]y=22\ hours[/tex]
Find the value of x
[tex]x=3y+2[/tex]
[tex]x=3*22+2[/tex]
[tex]x=68\ hours[/tex]
therefore
the answer is
Juliana worked [tex]68\ hours[/tex]
Can someone check my answer please?
Quadrilateral ABCD is inscribed in circle O.
What is m∠B?
m∠A + m∠B = 180°
2x - 7 + 2x + 3 = 180
4x - 4 = 180
4x = 184
x = 46
m∠B = 2x + 3
m∠B = 2(46) + 3
m∠B = 92 + 3
m∠B = 95°
Answers
The angles A and B do not add to 180°. Rather angles A and C add to 180°, because the sum of the measures of the arcs they intercept is 360°.
.. (2x -7) +(x+4) = 180
.. 3x = 183
.. x = 61
Then ∠B = (2*61 +3)° = 125°
_____
∠A = (2*61 -7)° = 115°
∠C = (61+4)° = 65°
∠D = 180° -125° = 55°
so ABCD is NOT a trapezoid..
If PQRS is a parallelogram, what is the value of Y
Answers
y = 13 * 4
y = 52
answer
C. 52
Answer:
52
Step-by-step explanation:
did the question
What is the volume of a cube whose edges each have a measure of 1.5 cm?
A)2.25 cm³
B)3.375 cm³
C)4.5 cm³
D)9 cm³
I saw this question and I realized that it had the wrong answer. The actual answer is 3.375cm
Answers
Hope this helped!
Solve the system of equations
y=3x+30
y=8x
_______________________
x= ??
y= ??
Answers
Since both equations are set equal to y, set 3x+30=8x. Subtract 3x from each side, getting 5x=30. Divide by 5, so x=6. Then, just plug in 6 for x in any of the two equations, so y=48.
y = 3x + 30
y = 8x
Since y = both the equations, we can equate them
8x = 3x + 30 {Take 3x by subtracting to the other side in order to find the value of the variable)
We do minus, when we see plus
8x - 3x = 3x - 3x + 30
3x and -3x cancels out in the right hand side
5x = 30
Divide by 5 on either side to isolate x
We do division, when we see multiplication
[tex] \frac{5x}{5} = \frac{30}{5} [/tex]
5 and 5 cancels out
x = 6
Now, we need to substitute x by 6 in order to find y
We can substitute in either equation, we will still get the same value
y = 8(6)
= 48
y = 3(6) + 30
= 18 + 30
= 48
x = 6 , y = 48
PLEASE HELP MEEEE
Describe the relationship of input and output values for composite functions.
Answers
IN A COMPOSITE FUNCTION f[g(x)], SOMETIMES WRITTEN (fog) (x), THE OUTPUT OF FUNCTION G IS THE INPUT TO FUNCTION F.
Lamar has a summer job. He gets paid $7.25 an hour and a $150 bonus at the end of summer. The total Lamar earns can be modeled by the equation f(h) = 7.25h + 150, where h is the number of hours he works. In what form is the equation?
Answers
Final answer:
The equation representing Lamar's summer job earnings is in linear form with a constant rate of change represented by 7.25 and a vertical intercept of 150, which is his end-of-summer bonus.
Explanation:
The equation provided, f(h) = 7.25h + 150, is in linear form. This type of equation is used to model a relationship where the dependent variable, f(h), which represents Lamar's earnings, changes at a constant rate with respect to the independent variable, h, which represents the number of hours worked. The number 7.25 represents Lamar's hourly wage, while the 150 represents a fixed bonus amount he receives at the end of the summer, making it the constant term or vertical intercept when graphed on a coordinate plane.
the diameter of a bike is 90cm. How far would it travel after 5 revolutions?
Answers
[length of a circumference]=2*pi*r
diameter=90 cm-------------> r=d/2--------> r=45 cm
[length of a circumference]=2*pi*45----------> 90*pi cm
with 1 revolution will go the length of the wheel
if 1 revolution is-------------------> 90*pi cm
5 revolution is--------------------> X
X=5*90*pi----------> 1413 cm
the answer is 1413 cm
26 POINTS WILL GIVE BRAINLIEST
2. Do the sides 16, 30, and 38 form a Pythagorean Triple? Explain why or why not.
3. A triangle has sides of length 10, 14, and 22. Is the triangle acute, right, or obtuse. Explain.
12. A person can see the top of a building at an angle of 42˚. The person is standing 30 ft away from the building and has an eye level of 6 ft. How tall is the building to the nearest tenth of a foot?
Answers
3. The tiangle is acute because it has all angles smaller than 90*
12: The buillding is approximately 100 ft tall give or take. I am sorry If i am wrong on the last one
Medals please help
Which of the following is the statement of the triangle inequality theorem?
A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
C. The longest side of a triangle is opposite the largest angle.
D. The largest angle of a triangle is between the two longest sides.,
Answers
The measures of exterior angles of a regular polygon with n numbers of sides ______ as n increases.
increases
decreases
remains the same,
Answers
how many 1020 flats can fit on (2) 8'x4' tables?
Answers
The dimensions of each 1020 flat is 11" by 22". We will convert the measurements of the table to inches. 8(12) = 96". 4(12) = 48". If we lay the longest edge of the flat side along the long edge of the table, 4 flats will fit along it with 8 inches left over. This would put the smaller edge of the flat along the smaller edge of the table, which would allow for 4 rows of 4, or 16 flats on each table. 16*2=32 flats between both tables.
This works out the same if we turn the flats around. Let the smaller edge of the flat, 11", be along the longer edge of the table, 96". This would allow for 8 flats. This puts the longer edge of the flat, 22", along the shorter edge of the table, 48"; this puts 2 rows of 8, which would be 16 flats on each table, for a total of 32 flats.
helppppppppppppppppppppppppp
Answers
x = 10 units
Explanation:
First, let's consider the smaller triangle.:
It is a right-angled triangle, therefore, we can use the special trig functions.
tan θ = opposite / adjacent
tan 45 = opposite / 5
opposite = 5
Now, for the larger triangle:
It is also a right angled triangle which means that we can use the special trig functions.
sin θ = opposite / hypotenuse
sin (30) = 5 / x
x = 10 units
Hope this helps :)
10 POINTS + BRAINLIEST ANSWER!!!
65x + y = 455
A grocery store receives a shipment of oranges and consistently sells the same number of oranges each day. The equation above models the number of oranges, y, that remain x days after the shipment is received. What does it mean that (7, 0) is a solution to the equation?
A. It takes 7 days after the shipment until none of the oranges are remaining.
B. There are 7 oranges in the shipment.
C. It takes 7 days for orange to be sold to 455 customers.
D. After the shipment, 7 oranges are sold each day.
Answers
Please Help
A motorcycle cost $12,000 when it was purchased. The value of a motorcycle decreases by 6% each year. Find the rate of decay each month and select the correct answer below.
−0.005143%
−0.5143%
−0.005%
−0.5%
Answers
If the rate of decay is 6% per year, that means the motorcycle retains 93% of its value every year. Because there are 12 months in a year, you can use the following equation:
x^12 = 0.94,
where x = the rate of decay each month, 12 = the number of months, and 0.94 = the retained value each year. Next, set a logarithmic function on each side as such:
LOG(x^12) = LOG(0.94)
When applying log functions, exponentials (like the 12 in the equation) are moved outside of the function like so:
LOG(x^12) = 12(LOG(x))
Therefore,
12(LOG(x)) = LOG(0.94) = -0.0268721464
When you divide both sides by 12, the equation becomes
LOG(x) = -0.00223934553
Finally, remove the LOG from the left side by applying both sides of the each by 10^() as such:
10^(LOG(X)) = 10^(-0.00223934553)
X = 0.994856987
Therefore, the motorcycle retains that 0.994856987 of its value every year.
1 - 0.994856987 = 0.005143
Expressed as a percentage, this value is 0.5143013%
The rate of decay each month is given by 0.5143% and this can be determined by forming the expression from the given data.
Given :
A motorcycle cost $12,000 when it was purchased.The value of a motorcycle decreases by 6% each year.There are 12 months in a year then the value motorcycle retains every year is:
[tex]x^{12}=0.94[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm logx^{12}=log(0.94)[/tex]
12 log x = log(0.94)
Now, divide log(0.94) by 12 in the above expression.
[tex]\rm log x = \dfrac{log(0.94)}{12}[/tex]
log x = -0.00223934553
[tex]x = 10^{-0.00223934553}[/tex]
x = 0.994856987
Now, to determine the rate of decay:
= (1 - x)100
= (1 - 0.994856987)100
= (0.005143)100
= 0.5143%
Therefore, the correct option is B).
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which equation has (2, -1) as a solution?
A. y = 2x - 1
B. y = x + 3
C. y = x - 3
D. y = -2x + 1
If someone could explain this to me it would be greatly appreciated. Thank you.
Answers
A. 2(2)-1 = 3 <>-1
B. 2+3 = 5<>-1
C. 2-3 = -1 = y
so C has (2,-1) as a solution
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
1. a root at 3i
2. a root at 2+4sqrt(3)
3. a root at -1/3
and that f(1)=-7520
Find polynomial f(x) as a product of its factors.
Given the three roots, we can conclude that the two other roots are the conjugates, namely -3i and 2-4sqrt(3).
Since
(x+3i)(x-3i)=x^2+9, and
(x-2+4sqrt(3))(x-2-4sqrt(3)=x^2-4x-44
We conclude that polynomial f(x) has the form
f(x)=a(x^2+9)(x^2-4x-44)(3x+1)
where a is a constant to be determined.
Knowing that f(1)=-7520, we can substitute x=1 in f(x) to get
-7520=a(1^2+9)(1^2-4(1)-44)(3+1)=a(10)(-47)(4)
=>
a=-7520/(-1880)=4
Therefore the polynomial f(x) is defined as
f(x)=4(x^2+9)(x^2-4x-44)(3x+1)
or
f(x)=4(3x+1)(x^2+9)(x^2-4x-44)
The root at 3i means that (x -3i)*(x +3i) = (x^2 +9) is a factor.
The root at 2 +4√3 means that (x -2 -4√3)*(x -2 +4√3) = (x^2 -4x -44) is a factor.
Evaluated at x=1, the product of these factors is (4)*(10)*(-47) = -1880, so there is an additional factor of -7520/-1880 = 4.
The intercept form of the polynomial is
.. y = 4(3x +1)*(x^2 +9)*(x^2 -4x -44)
helppppppppppppppppppppppppp
Answers
[tex] \frac{y2-y1}{x2-x1} [/tex]
[tex] \frac{5-1}{-2-3} [/tex]
[tex] \frac{4}{-5} [/tex]
So -4/5 is the right answer.
Hope this helps :)
The area of a rectangular hotel room is 209 square feet. the perimeter is 60 feet. what are the dimensions of the room?
Answers
B) 2x + 2y = 60
A) y = 209 / x putting this into equation B
B) 2x + (2 * 209 / x) = 60
2x + 418 / x = 60 multiplying by x
2x^2 + 418 = 60x
2x^2 -60x + 418 = 0
Solving by quadratic formula
x = 19
y = 11
answer asap Malia created a correct function table using the equation g = 4f.
Which table could be Malia's?
A.
B.
C.
Answers
hope I helped
Hey, if I could get some help on this i'd really appreciate it.
QUESTION 1
What is the constant of variation for the quadratic variation?
0.1y = 3x^2
0.03
0.1
30
3
QUESTION 2
What is the constant of variation for the quadratic variation?
10y = 6x2
6
1.6
10
0.6
QUESTION 3
If f(x) varies directly with x^2, and f(x) = 96 when x = 4, find the value of f(2).
32
24
72
192
QUESTION 4
Write a quadratic variation equation if g(x) varies directly with x^2, and g(x) = 98 when x = 7.
g(x) = 2x^2
g(x) = 7x^2
g(x) = 1/2x^2
g(x) = 14x^2
Answers
.. y = kx^2
The value of k is 3/0.1 = 30.
2) When you rewrite the equation as
.. y = kx^2
The value of k is 6/10 = 0.6.
3) f(x) = kx^2
.. k = f(x)/x^2 = 96/4^2 = f(2)/2^2
.. f(2) = 96(2/4)^2
.. f(2) = 24
4) g(x) = kx^2
.. 98 = k*7^2 = 49k
.. k = 98/49 = 2
g(x) = 2x^2
In the United States the speed limit signs are in miles per hour. Unfortunately, your speedometer only reads in km/hour. How fast are you allowed to go if the speed sign says 70 mph (rounded to the nearest hundredth)
Answers
Answer:
The speed limit will be 112.65 kph.
Step-by-step explanation:
In order to find how fast one can go when speed sign says 70mph and the speedometer reads in km per hour we convert mph to kmph.
The conversion unit is 1mph= 1.609344kph
So 70mph = 70x1.609344=112.6541kph
Or 70mph=112.65 kph
One can travel at 112.65 kph.
Identify the factors of 9x2 + 30x + 25.
A) (3x − 5)(3x − 5)
B) (3x + 5)(3x + 5)
C) (9x + 5)(x + 5)
D) (9x − 5)(x − 5)
Answers
_____
The signs of the coefficients tell you the binomial factors must have both signs positive (selections B and C only). Selection B produces an x-term that is 15x+15x=30x (as we want); selection C produces an x-term that is 45x+5x=50x (not what we want).
Answer:
B is correct
Step-by-step explanation:
The signs of the coefficients tell you the binomial factors must have both signs positive (selections B and C only). Selection B produces an x-term that is 15x+15x=30x (as we want); selection C produces an x-term that is 45x+5x=50x (not what we want).